A spin-statistics theorem for certain topological geons

Abstract

We review the mechanism in quantum gravity whereby topological geons, particles made from non-trivial spatial topology, are endowed with non-trivial spin and statistics. In a theory without topology change there is no obstruction to `anomalous' spin-statistics pairings for geons. However, in a sum-over-histories formulation including topology change, we show that non-chiral Abelian geons do satisfy a spin-statistics correlation if they are described by a wavefunction which is given by a functional integral over metrics on a particular 4-manifold. This manifold describes a topology changing process which creates a pair of geons from R^3.